Finite Group Databasebeta

← Group #306927

Character table — Group #306927

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888882
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-111-1-1-1-1-1
χ31111111111111111111111111111-1-111111111-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1-1-1111-1-1-111-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-111-1-1-1-11-1-1111-1-1-1-1-1-1111
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111-1-1111
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111111111-1-1-1
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11
χ1011111111111111111-1-1-1-111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1
χ1111111111111111111-1-1-1-111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-11-1-1-1-11111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-11111-111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111111-1-111-111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111111-1-11-1-1-1-111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-111-1-1-11111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-111-1-111111-1-111-1
χ17222222222-22-22-22-2-20000-22222000022-2-2-2-2-2-2000000000000000002000000000
χ18222222222-22-22-22-2-20000-222220000-2-22222-2-200000000000000000-2000000000
χ19222222222-22-22-22-2-20000-2-2-2-2-200002222-2-22200000000000000000-2000000000
χ20222222222-22-22-22-2-20000-2-2-2-2-20000-2-2-2-22222000000000000000002000000000
χ2122222222-22-22-22-22-22222-20000-2-22200000000-2-20000220000-200000000000000
χ2222222222-22-22-22-22-22222-20000-2-2-2-200000000220000-2-20000200000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000222200000000220000-2-20000-200000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000022-2-200000000-2-20000220000200000000000000
χ252222-2-2-2-22-2-222-2-22-222-2-2200002-200000000000000000000000000002i−2i002i−2i000
χ262222-2-2-2-22-2-222-2-22-222-2-2200002-20000000000000000000000000000−2i2i00−2i2i000
χ272222-2-2-2-22-2-222-2-22-2-2-22220000-2200000000000000000000000000002i−2i00−2i2i000
χ282222-2-2-2-22-2-222-2-22-2-2-22220000-220000000000000000000000000000−2i2i002i−2i000
χ292222-2-2-2-2-222-2-222-2-200002000000002i−2i002i−2i000022-2-20000000002i−2i0000000000
χ302222-2-2-2-2-222-2-222-2-200002000000002i−2i002i−2i0000-2-222000000000−2i2i0000000000
χ312222-2-2-2-2-222-2-222-2-20000200000000−2i2i00−2i2i000022-2-2000000000−2i2i0000000000
χ322222-2-2-2-2-222-2-222-2-20000200000000−2i2i00−2i2i0000-2-2220000000002i−2i0000000000
χ332222-2-2-2-2-2-222-2-222222-2-2-20000-22002i−2i00−2i2i0000000000000002i−2i000000000000
χ342222-2-2-2-2-2-222-2-222222-2-2-20000-2200−2i2i002i−2i000000000000000−2i2i000000000000
χ352222-2-2-2-2-2-222-2-2222-2-222-200002-2002i−2i00−2i2i000000000000000−2i2i000000000000
χ362222-2-2-2-2-2-222-2-2222-2-222-200002-200−2i2i002i−2i0000000000000002i−2i000000000000
χ3722-2-22-2-2202020-20-202i−2i2i−2i022−2−2002-20000002−200i2−i2i2−i22i−2ii2i2−i2−i2000000002−200000
χ3822-2-22-2-2202020-20-202i−2i2i−2i022−2−200-220000002−200i2−i2i2−i2−2i2i−i2−i2i2i200000000−2200000
χ3922-2-22-2-2202020-20-202i−2i2i−2i0−2−222002-2000000−2200−i2i2−i2i22i−2i−i2−i2i2i200000000−2200000
χ4022-2-22-2-2202020-20-202i−2i2i−2i0−2−22200-22000000−2200−i2i2−i2i2−2i2ii2i2−i2−i2000000002−200000
χ4122-2-22-2-2202020-20-20−2i2i−2i2i022−2−2002-20000002−200−i2i2−i2i2−2i2i−i2−i2i2i2000000002−200000
χ4222-2-22-2-2202020-20-20−2i2i−2i2i022−2−200-220000002−200−i2i2−i2i22i−2ii2i2−i2−i200000000−2200000
χ4322-2-22-2-2202020-20-20−2i2i−2i2i0−2−222002-2000000−2200i2−i2i2−i2−2i2ii2i2−i2−i200000000−2200000
χ4422-2-22-2-2202020-20-20−2i2i−2i2i0−2−22200-22000000−2200i2−i2i2−i22i−2i−i2−i2i2i2000000002−200000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ464444-4-4-4-444-4-444-4-440000-40000000000000000000000000000000000000000000
χ4744-4-44-4-440-40-404040000002222−22−220000000000−2222000000000000000000000000000
χ4844-4-44-4-440-40-40404000000−22−222222000000000022−22000000000000000000000000000
χ4944-4-4-444-4040-40-4040000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5044-4-4-444-4040-40-404000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ5144-4-4-444-40-404040-404i−4i−4i4i00000000000000000000000000000000000000000000
χ5244-4-4-444-40-404040-40−4i4i4i−4i00000000000000000000000000000000000000000000
χ534-44-444-4-4000000000000002i2−2i22i2−2i20000000000002i2−2i20000002-22-2000000000000000
χ544-44-444-4-4000000000000002i2−2i22i2−2i2000000000000−2i22i2000000-22-22000000000000000
χ554-44-444-4-400000000000000−2i22i2−2i22i20000000000002i2−2i2000000-22-22000000000000000
χ564-44-444-4-400000000000000−2i22i2−2i22i2000000000000−2i22i20000002-22-2000000000000000
χ574-4-444-44-440-40-40400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ584-4-444-44-440-40-4040000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ594-4-444-44-4-404040-400000004i−4i−4i4i000000000000000000000000000000000000000
χ604-4-444-44-4-404040-40000000−4i4i4i−4i000000000000000000000000000000000000000
χ614-4-44-44-444040-40-4000000000000000004i−4i0000000000000000000000000000000
χ624-4-44-44-444040-40-400000000000000000−4i4i0000000000000000000000000000000
χ634-4-44-44-44-40-404040000000000000000000000000000000000000000000000022−220
χ644-4-44-44-44-40-4040400000000000000000000000000000000000000000000000−22220
χ658-88-8-8-888000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).